If you draw a card with a value of four or less from a standard deck of cards, I will pay you $162. If not, you pay me $45. (Aces are considered the highest card in the deck.) Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

2.77

The expected value is positive, so you expect to gain on average $2.77 per draw.

Explanation:

Define two events

W = winning = getting a card 4 or less

L = losing = getting 5 or higher

P(W) = probability of winning

P(W) = 12/52 since there are 12 cards that are four or less out of 52

P(W) = 3/13 for any suit of 13, there are 3 cards that are four or less

P(L) = 1-P(W)

P(L) = 1-3/13

P(L) = 13/13 - 3/13

P(L) = 10/13

V(W) = net value of winning

V(W) = 162

V(L) = net value of losing

V(L) = -45

E(X) = expected value

E(X) = P(W)*V(W) + P(L)*V(L)

E(X) = (3/13)*162 + (10/13)*(-45)

E(X) = 36/13

E(X) = 2.76923076923077

E(X) = 2.77 rounding to two decimal places (to the nearest cent)

This game is in favor to the player since we got a positive expected value. A fair game would occur if the expected value was 0.

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation:

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.